I did some testing today to see if I could get some more data points.
For reference, I'm running on a GT710 I ripped out of my media PC after my primary card died, so it's sitting on 1 GB of VRAM and is all sorts of not great for gaming.
If I launch Starsector as soon as my computer launches windows, I have a lot of leeway in the number of mods I can use and even with saving every time the autosave mod pokes me, I can play for hours without crashing on a save. Now that I think about it, if I manage to save a couple of times, I've never crashed after that.
On the other hand, if Starsector has already been played on the current boot, even if it ran fine, launching it again seems to make things iffy. I still only crash on saving mind you, but I do so almost every time I try, be it creating a new character or loading and saving an existing one. If I remove literally every faction mod, I no longer run into this.
Having GraphicsLib active or not does not seem to impact it at all, which feels weird.